12a
0769
(K12a
0769
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 9 11 2 6 1 7 5 4
Solving Sequence
2,7
8 3
1,11
6 9 5 10 4 12
c
7
c
2
c
1
c
6
c
8
c
5
c
10
c
3
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.90028 × 10
221
u
119
− 6.36136 × 10
221
u
118
+ ··· + 3.32809 × 10
221
b − 7.62938 × 10
223
,
6.58487 × 10
222
u
119
− 1.43090 × 10
222
u
118
+ ··· + 1.05389 × 10
222
a − 5.06564 × 10
224
,
u
120
− u
119
+ ··· − 55u + 76i
I
u
2
= h43u
25
+ 128u
24
+ ··· + 49b − 207, 235u
25
+ 246u
24
+ ··· + 49a − 443, u
26
− 5u
24
+ ··· − 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 146 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h4.90 × 10
221
u
119
− 6.36 × 10
221
u
118
+ · · · + 3.33 × 10
221
b − 7.63 ×
10
223
, 6.58 × 10
222
u
119
− 1.43 × 10
222
u
118
+ · · · + 1.05 × 10
222
a − 5.07 ×
10
224
, u
120
− u
119
+ · · · − 55u + 76i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−6.24813u
119
+ 1.35773u
118
+ ··· + 43.1116u + 480.660
−1.47240u
119
+ 1.91142u
118
+ ··· + 144.938u + 229.242
a
6
=
−5.70471u
119
− 0.638481u
118
+ ··· − 97.4784u + 319.351
−4.92763u
119
+ 0.244041u
118
+ ··· − 31.4329u + 326.770
a
9
=
−7.17248u
119
+ 1.42733u
118
+ ··· + 47.5668u + 545.642
−2.50902u
119
+ 2.36297u
118
+ ··· + 177.669u + 326.769
a
5
=
−7.55899u
119
− 0.806060u
118
+ ··· − 153.369u + 406.441
−4.70727u
119
+ 0.223186u
118
+ ··· − 30.9319u + 305.682
a
10
=
−4.77573u
119
− 0.553687u
118
+ ··· − 101.826u + 251.418
−1.47240u
119
+ 1.91142u
118
+ ··· + 144.938u + 229.242
a
4
=
−6.42549u
119
− 0.253055u
118
+ ··· − 48.4915u + 394.825
−3.76726u
119
+ 0.426794u
118
+ ··· + 2.87528u + 263.024
a
12
=
4.90188u
119
− 3.66164u
118
+ ··· − 345.185u − 620.459
0.318017u
119
− 1.90163u
118
+ ··· − 189.757u − 184.421
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11.9826u
119
− 3.58926u
118
+ ··· − 186.522u − 990.154
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
120
+ 49u
119
+ ··· + 96657u + 5776
c
2
, c
7
u
120
+ u
119
+ ··· + 55u + 76
c
3
u
120
+ 15u
118
+ ··· + 8192u + 1024
c
4
, c
11
, c
12
u
120
+ 3u
119
+ ··· + u + 2
c
5
, c
8
u
120
− 4u
119
+ ··· − 288u + 112
c
6
, c
10
u
120
− u
119
+ ··· + 10311u + 1766
c
9
u
120
− 7u
119
+ ··· + 3752u + 928
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
120
+ 43y
119
+ ··· + 814266207y + 33362176
c
2
, c
7
y
120
− 49y
119
+ ··· − 96657y + 5776
c
3
y
120
+ 30y
119
+ ··· + 22020096y + 1048576
c
4
, c
11
, c
12
y
120
+ 123y
119
+ ··· + 311y + 4
c
5
, c
8
y
120
+ 68y
119
+ ··· + 688512y + 12544
c
6
, c
10
y
120
+ 83y
119
+ ··· + 16685179y + 3118756
c
9
y
120
+ y
119
+ ··· − 8464960y + 861184
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.640376 + 0.754506I
a = −0.273310 − 0.956734I
b = 1.042890 − 0.294443I
5.13060 + 2.11657I 0
u = 0.640376 − 0.754506I
a = −0.273310 + 0.956734I
b = 1.042890 + 0.294443I
5.13060 − 2.11657I 0
u = −0.526278 + 0.835444I
a = 0.404937 − 0.002448I
b = −0.290883 + 1.201140I
−7.92215 − 4.97148I 0
u = −0.526278 − 0.835444I
a = 0.404937 + 0.002448I
b = −0.290883 − 1.201140I
−7.92215 + 4.97148I 0
u = 0.882437 + 0.436290I
a = −1.72646 − 2.00320I
b = −0.14486 − 2.24214I
−10.71680 − 1.79302I 0
u = 0.882437 − 0.436290I
a = −1.72646 + 2.00320I
b = −0.14486 + 2.24214I
−10.71680 + 1.79302I 0
u = −0.895202 + 0.495352I
a = −0.94608 + 2.31227I
b = 0.087800 + 1.396210I
−1.78369 + 2.17868I 0
u = −0.895202 − 0.495352I
a = −0.94608 − 2.31227I
b = 0.087800 − 1.396210I
−1.78369 − 2.17868I 0
u = 0.914841 + 0.478429I
a = 1.52846 + 1.20791I
b = −0.378324 + 1.071270I
−1.78722 − 2.37288I 0
u = 0.914841 − 0.478429I
a = 1.52846 − 1.20791I
b = −0.378324 − 1.071270I
−1.78722 + 2.37288I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832669 + 0.489433I
a = −0.35939 + 1.69937I
b = −0.358930 + 1.273050I
−1.56898 + 1.83315I 0
u = −0.832669 − 0.489433I
a = −0.35939 − 1.69937I
b = −0.358930 − 1.273050I
−1.56898 − 1.83315I 0
u = 0.883036 + 0.381686I
a = 0.189734 + 0.020446I
b = 0.499406 + 0.462228I
−1.35072 − 1.18683I 0
u = 0.883036 − 0.381686I
a = 0.189734 − 0.020446I
b = 0.499406 − 0.462228I
−1.35072 + 1.18683I 0
u = 0.809652 + 0.656870I
a = 0.848716 + 0.218807I
b = −0.720338 + 0.598197I
−1.31759 − 1.23542I 0
u = 0.809652 − 0.656870I
a = 0.848716 − 0.218807I
b = −0.720338 − 0.598197I
−1.31759 + 1.23542I 0
u = −0.872320 + 0.393222I
a = 2.21646 − 1.59565I
b = −0.065607 − 0.821017I
0.041033 − 0.859294I 0
u = −0.872320 − 0.393222I
a = 2.21646 + 1.59565I
b = −0.065607 + 0.821017I
0.041033 + 0.859294I 0
u = −1.034920 + 0.226485I
a = 0.853083 − 0.590111I
b = 0.801681 − 0.687458I
−6.96211 + 0.05806I 0
u = −1.034920 − 0.226485I
a = 0.853083 + 0.590111I
b = 0.801681 + 0.687458I
−6.96211 − 0.05806I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.472677 + 0.954639I
a = −0.039591 + 0.315286I
b = 0.66236 + 1.30816I
−4.59021 + 12.29690I 0
u = 0.472677 − 0.954639I
a = −0.039591 − 0.315286I
b = 0.66236 − 1.30816I
−4.59021 − 12.29690I 0
u = −0.695176 + 0.610567I
a = 0.837440 + 0.424941I
b = −0.607307 + 0.978322I
−2.45014 − 3.81871I 0
u = −0.695176 − 0.610567I
a = 0.837440 − 0.424941I
b = −0.607307 − 0.978322I
−2.45014 + 3.81871I 0
u = 0.937857 + 0.536832I
a = −1.29364 − 2.46504I
b = 0.381221 − 1.189800I
1.04041 − 5.59127I 0
u = 0.937857 − 0.536832I
a = −1.29364 + 2.46504I
b = 0.381221 + 1.189800I
1.04041 + 5.59127I 0
u = −0.466942 + 0.975547I
a = 0.032907 − 0.446919I
b = 0.580562 − 1.221380I
2.18598 − 7.87003I 0
u = −0.466942 − 0.975547I
a = 0.032907 + 0.446919I
b = 0.580562 + 1.221380I
2.18598 + 7.87003I 0
u = −0.972631 + 0.474931I
a = −0.478168 + 0.389429I
b = 0.495723 − 0.238417I
−0.55152 + 4.16383I 0
u = −0.972631 − 0.474931I
a = −0.478168 − 0.389429I
b = 0.495723 + 0.238417I
−0.55152 − 4.16383I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845008 + 0.351940I
a = 2.45288 + 2.44208I
b = 0.111293 + 0.735777I
−4.95807 + 3.90695I 0
u = 0.845008 − 0.351940I
a = 2.45288 − 2.44208I
b = 0.111293 − 0.735777I
−4.95807 − 3.90695I 0
u = −0.578766 + 0.699373I
a = −0.472636 + 1.200260I
b = 1.290760 + 0.327675I
−1.33795 − 5.57386I 0
u = −0.578766 − 0.699373I
a = −0.472636 − 1.200260I
b = 1.290760 − 0.327675I
−1.33795 + 5.57386I 0
u = 0.886943 + 0.175895I
a = −0.613692 + 0.718318I
b = −1.198730 − 0.548916I
−5.60557 + 5.04751I 0
u = 0.886943 − 0.175895I
a = −0.613692 − 0.718318I
b = −1.198730 + 0.548916I
−5.60557 − 5.04751I 0
u = 0.739706 + 0.509645I
a = 0.332396 − 0.867037I
b = −0.575450 − 1.044550I
1.69152 + 1.31290I 0
u = 0.739706 − 0.509645I
a = 0.332396 + 0.867037I
b = −0.575450 + 1.044550I
1.69152 − 1.31290I 0
u = −0.747119 + 0.815803I
a = −0.086094 + 0.707533I
b = 0.621373 + 0.213296I
4.69145 + 2.28641I 0
u = −0.747119 − 0.815803I
a = −0.086094 − 0.707533I
b = 0.621373 − 0.213296I
4.69145 − 2.28641I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.015460 + 0.447308I
a = −1.317700 − 0.432286I
b = 0.237227 + 0.107181I
−5.79389 − 7.01675I 0
u = 1.015460 − 0.447308I
a = −1.317700 + 0.432286I
b = 0.237227 − 0.107181I
−5.79389 + 7.01675I 0
u = 0.455745 + 0.753757I
a = 0.508301 − 0.127039I
b = −0.326725 − 0.980508I
−1.21124 + 2.82506I 0
u = 0.455745 − 0.753757I
a = 0.508301 + 0.127039I
b = −0.326725 + 0.980508I
−1.21124 − 2.82506I 0
u = 1.070650 + 0.334394I
a = 1.11732 + 1.32635I
b = 0.442128 + 1.240410I
−2.93359 − 0.36031I 0
u = 1.070650 − 0.334394I
a = 1.11732 − 1.32635I
b = 0.442128 − 1.240410I
−2.93359 + 0.36031I 0
u = −0.958174 + 0.583219I
a = −1.68183 + 2.25035I
b = 0.511496 + 1.072450I
−3.26276 + 8.54514I 0
u = −0.958174 − 0.583219I
a = −1.68183 − 2.25035I
b = 0.511496 − 1.072450I
−3.26276 − 8.54514I 0
u = −0.988511 + 0.551859I
a = 1.36500 − 1.43555I
b = −0.47857 − 1.64419I
−9.67224 + 2.94134I 0
u = −0.988511 − 0.551859I
a = 1.36500 + 1.43555I
b = −0.47857 + 1.64419I
−9.67224 − 2.94134I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885154 + 0.709753I
a = 0.272074 − 0.779465I
b = 0.640083 + 0.500521I
−1.51750 − 4.05330I 0
u = 0.885154 − 0.709753I
a = 0.272074 + 0.779465I
b = 0.640083 − 0.500521I
−1.51750 + 4.05330I 0
u = −0.150218 + 1.125420I
a = 0.234940 + 0.606687I
b = 0.177560 + 0.897894I
1.59223 + 0.82756I 0
u = −0.150218 − 1.125420I
a = 0.234940 − 0.606687I
b = 0.177560 − 0.897894I
1.59223 − 0.82756I 0
u = −0.478342 + 0.702792I
a = 0.559900 + 0.148553I
b = 0.205940 − 1.327080I
−8.23370 + 1.80575I 0
u = −0.478342 − 0.702792I
a = 0.559900 − 0.148553I
b = 0.205940 + 1.327080I
−8.23370 − 1.80575I 0
u = 1.162960 + 0.015963I
a = −0.17549 + 2.26357I
b = 0.16472 + 1.48066I
−13.9002 + 3.2371I 0
u = 1.162960 − 0.015963I
a = −0.17549 − 2.26357I
b = 0.16472 − 1.48066I
−13.9002 − 3.2371I 0
u = −0.878585 + 0.772283I
a = 0.365079 + 0.400564I
b = −0.041316 − 0.479766I
4.22944 + 2.91051I 0
u = −0.878585 − 0.772283I
a = 0.365079 − 0.400564I
b = −0.041316 + 0.479766I
4.22944 − 2.91051I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.120880 + 0.344185I
a = 0.07241 − 1.61285I
b = 0.108071 − 0.859897I
−6.25035 + 0.01892I 0
u = −1.120880 − 0.344185I
a = 0.07241 + 1.61285I
b = 0.108071 + 0.859897I
−6.25035 − 0.01892I 0
u = −1.117730 + 0.361741I
a = 1.32383 − 1.24388I
b = 0.53827 − 1.51484I
−8.26977 − 0.16688I 0
u = −1.117730 − 0.361741I
a = 1.32383 + 1.24388I
b = 0.53827 + 1.51484I
−8.26977 + 0.16688I 0
u = −1.061330 + 0.508158I
a = −0.89192 + 1.97682I
b = 0.85279 + 1.14210I
−1.81518 + 6.56693I 0
u = −1.061330 − 0.508158I
a = −0.89192 − 1.97682I
b = 0.85279 − 1.14210I
−1.81518 − 6.56693I 0
u = 1.082650 + 0.461042I
a = −0.72573 − 2.16920I
b = 1.03655 − 1.34819I
−7.66656 − 7.57137I 0
u = 1.082650 − 0.461042I
a = −0.72573 + 2.16920I
b = 1.03655 + 1.34819I
−7.66656 + 7.57137I 0
u = 0.874346 + 0.790463I
a = 0.615703 − 0.470871I
b = −0.078613 + 0.882615I
−0.00142 − 2.96056I 0
u = 0.874346 − 0.790463I
a = 0.615703 + 0.470871I
b = −0.078613 − 0.882615I
−0.00142 + 2.96056I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.947454 + 0.705336I
a = 0.050044 − 0.235893I
b = −0.756499 − 0.099528I
4.04803 + 3.39775I 0
u = −0.947454 − 0.705336I
a = 0.050044 + 0.235893I
b = −0.756499 + 0.099528I
4.04803 − 3.39775I 0
u = 0.510655 + 1.067890I
a = −0.020351 − 0.392987I
b = 0.263141 − 1.006270I
−4.23224 − 6.56669I 0
u = 0.510655 − 1.067890I
a = −0.020351 + 0.392987I
b = 0.263141 + 1.006270I
−4.23224 + 6.56669I 0
u = −1.024770 + 0.614403I
a = −0.543083 − 0.844425I
b = −1.55541 + 0.18806I
−2.67491 + 10.64940I 0
u = −1.024770 − 0.614403I
a = −0.543083 + 0.844425I
b = −1.55541 − 0.18806I
−2.67491 − 10.64940I 0
u = 1.004810 + 0.652032I
a = −0.325232 + 0.602839I
b = −1.225640 − 0.112802I
4.01972 − 7.46198I 0
u = 1.004810 − 0.652032I
a = −0.325232 − 0.602839I
b = −1.225640 + 0.112802I
4.01972 + 7.46198I 0
u = 0.489454 + 1.098110I
a = 0.226348 + 0.610901I
b = 0.376642 + 1.161960I
1.92369 + 1.64383I 0
u = 0.489454 − 1.098110I
a = 0.226348 − 0.610901I
b = 0.376642 − 1.161960I
1.92369 − 1.64383I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.203110 + 0.141860I
a = −0.01063 − 1.99891I
b = 0.047918 − 1.218620I
−6.29656 − 0.50343I 0
u = −1.203110 − 0.141860I
a = −0.01063 + 1.99891I
b = 0.047918 + 1.218620I
−6.29656 + 0.50343I 0
u = 1.088030 + 0.538755I
a = −0.62773 − 1.56135I
b = 0.931399 − 0.613542I
−5.08544 − 6.87789I 0
u = 1.088030 − 0.538755I
a = −0.62773 + 1.56135I
b = 0.931399 + 0.613542I
−5.08544 + 6.87789I 0
u = 0.679820 + 0.336957I
a = 1.232030 − 0.681094I
b = −0.406069 + 0.398167I
−1.81621 − 1.39548I 0. + 4.94228I
u = 0.679820 − 0.336957I
a = 1.232030 + 0.681094I
b = −0.406069 − 0.398167I
−1.81621 + 1.39548I 0. − 4.94228I
u = 1.088030 + 0.622795I
a = −1.35243 − 1.36217I
b = 0.445681 − 1.106640I
−3.05949 − 8.07209I 0
u = 1.088030 − 0.622795I
a = −1.35243 + 1.36217I
b = 0.445681 + 1.106640I
−3.05949 + 8.07209I 0
u = 0.337789 + 0.657214I
a = 0.819345 + 0.033021I
b = −0.839678 − 0.535416I
−2.95335 + 2.23609I 2.00000 − 1.76365I
u = 0.337789 − 0.657214I
a = 0.819345 − 0.033021I
b = −0.839678 + 0.535416I
−2.95335 − 2.23609I 2.00000 + 1.76365I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.087990 + 0.666342I
a = −1.51101 + 1.19215I
b = 0.428378 + 1.252690I
−9.6150 + 10.5872I 0
u = −1.087990 − 0.666342I
a = −1.51101 − 1.19215I
b = 0.428378 − 1.252690I
−9.6150 − 10.5872I 0
u = −0.692575 + 0.103205I
a = −0.006438 − 0.545981I
b = −0.783820 + 0.630029I
0.33138 − 2.81172I −1.59494 + 8.15444I
u = −0.692575 − 0.103205I
a = −0.006438 + 0.545981I
b = −0.783820 − 0.630029I
0.33138 + 2.81172I −1.59494 − 8.15444I
u = −1.173680 + 0.559139I
a = −0.97992 + 1.25670I
b = 0.214798 + 0.833089I
−1.67878 + 4.55618I 0
u = −1.173680 − 0.559139I
a = −0.97992 − 1.25670I
b = 0.214798 − 0.833089I
−1.67878 − 4.55618I 0
u = −0.130840 + 0.683948I
a = 0.689722 − 1.176870I
b = 0.387314 − 0.530088I
−2.97731 + 3.82183I 1.37005 − 2.48592I
u = −0.130840 − 0.683948I
a = 0.689722 + 1.176870I
b = 0.387314 + 0.530088I
−2.97731 − 3.82183I 1.37005 + 2.48592I
u = −1.311010 + 0.004264I
a = −0.42932 − 1.89199I
b = −0.383741 − 1.340220I
−11.3531 + 9.5454I 0
u = −1.311010 − 0.004264I
a = −0.42932 + 1.89199I
b = −0.383741 + 1.340220I
−11.3531 − 9.5454I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031930 + 0.824659I
a = 0.92437 − 1.11266I
b = −0.09117 − 1.52498I
−8.87470 + 3.23927I 0
u = −1.031930 − 0.824659I
a = 0.92437 + 1.11266I
b = −0.09117 + 1.52498I
−8.87470 − 3.23927I 0
u = 1.147360 + 0.682433I
a = 1.05738 + 1.77093I
b = −0.71682 + 1.42364I
−6.6712 − 18.2695I 0
u = 1.147360 − 0.682433I
a = 1.05738 − 1.77093I
b = −0.71682 − 1.42364I
−6.6712 + 18.2695I 0
u = −1.152220 + 0.686593I
a = 0.97380 − 1.74188I
b = −0.61990 − 1.36344I
0.06823 + 13.90220I 0
u = −1.152220 − 0.686593I
a = 0.97380 + 1.74188I
b = −0.61990 + 1.36344I
0.06823 − 13.90220I 0
u = 1.342350 + 0.051845I
a = −0.28993 + 1.82104I
b = −0.242137 + 1.218030I
−4.87573 − 4.97897I 0
u = 1.342350 − 0.051845I
a = −0.28993 − 1.82104I
b = −0.242137 − 1.218030I
−4.87573 + 4.97897I 0
u = 1.166220 + 0.708331I
a = 0.85639 + 1.62895I
b = −0.455418 + 1.336690I
−0.25747 − 8.00434I 0
u = 1.166220 − 0.708331I
a = 0.85639 − 1.62895I
b = −0.455418 − 1.336690I
−0.25747 + 8.00434I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.496518 + 0.387230I
a = 0.638984 − 0.276542I
b = 0.003814 + 0.743880I
−0.95945 − 1.26307I −1.11291 + 4.67551I
u = 0.496518 − 0.387230I
a = 0.638984 + 0.276542I
b = 0.003814 − 0.743880I
−0.95945 + 1.26307I −1.11291 − 4.67551I
u = 0.030638 + 0.627848I
a = 0.630163 + 0.281169I
b = −0.705482 − 1.181490I
−4.93792 + 3.70699I −0.95537 − 2.54574I
u = 0.030638 − 0.627848I
a = 0.630163 − 0.281169I
b = −0.705482 + 1.181490I
−4.93792 − 3.70699I −0.95537 + 2.54574I
u = −0.368109 + 0.489191I
a = 0.940791 + 0.181536I
b = −0.351242 + 0.085606I
1.128240 − 0.421422I 8.38329 + 0.77170I
u = −0.368109 − 0.489191I
a = 0.940791 − 0.181536I
b = −0.351242 − 0.085606I
1.128240 + 0.421422I 8.38329 − 0.77170I
u = 1.24385 + 0.68095I
a = −0.892938 − 0.924431I
b = −0.035336 − 0.993557I
−6.66799 + 0.06763I 0
u = 1.24385 − 0.68095I
a = −0.892938 + 0.924431I
b = −0.035336 + 0.993557I
−6.66799 − 0.06763I 0
u = −0.185544 + 0.477522I
a = 0.577402 − 0.178656I
b = −0.654975 + 0.931972I
0.28814 − 2.49618I 0.33548 + 5.38020I
u = −0.185544 − 0.477522I
a = 0.577402 + 0.178656I
b = −0.654975 − 0.931972I
0.28814 + 2.49618I 0.33548 − 5.38020I
16
II. I
u
2
= h43u
25
+ 128u
24
+ · · · + 49b − 207, 235u
25
+ 246u
24
+ · · · + 49a −
443, u
26
− 5u
24
+ · · · − 6u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−4.79592u
25
− 5.02041u
24
+ ··· + 6.59184u + 9.04082
−0.877551u
25
− 2.61224u
24
+ ··· + 2.75510u + 4.22449
a
6
=
0.0816327u
25
− 2.40816u
24
+ ··· − 1.16327u + 3.81633
−0.0816327u
25
+ 1.40816u
24
+ ··· − 2.83673u − 2.81633
a
9
=
−2.91837u
25
− 2.40816u
24
+ ··· + 3.83673u + 4.81633
−0.877551u
25
− 2.61224u
24
+ ··· + 2.75510u + 4.22449
a
5
=
6.48980u
25
+ 4.55102u
24
+ ··· − 5.97959u − 7.10204
13
7
u
25
+
19
7
u
24
+ ··· −
33
7
u −
31
7
a
10
=
−3.91837u
25
− 2.40816u
24
+ ··· + 3.83673u + 4.81633
−0.877551u
25
− 2.61224u
24
+ ··· + 2.75510u + 4.22449
a
4
=
−8.67347u
25
− 7.63265u
24
+ ··· + 10.3469u + 7.26531
−u
22
+ 4u
20
+ ··· + 5u
2
− 1
a
12
=
−
3
7
u
25
+
8
7
u
24
+ ··· +
34
7
u +
12
7
−3.89796u
25
− 1.51020u
24
+ ··· + 7.79592u + 4.02041
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16
49
u
25
+
67
49
u
24
+ ··· −
816
49
u +
160
49
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 10u
25
+ ··· − 12u + 1
c
2
u
26
− 5u
24
+ ··· − 6u
2
+ 1
c
3
u
26
+ u
25
+ ··· − 6u + 1
c
4
u
26
− 2u
25
+ ··· − 2u + 1
c
5
u
26
− 3u
25
+ ··· + 13u
2
+ 1
c
6
u
26
+ 13u
24
+ ··· + 3u + 1
c
7
u
26
− 5u
24
+ ··· − 6u
2
+ 1
c
8
u
26
+ 3u
25
+ ··· + 13u
2
+ 1
c
9
u
26
− 4u
24
+ ··· + 8u
2
+ 1
c
10
u
26
+ 13u
24
+ ··· − 3u + 1
c
11
, c
12
u
26
+ 2u
25
+ ··· + 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 10y
25
+ ··· + 8y + 1
c
2
, c
7
y
26
− 10y
25
+ ··· − 12y + 1
c
3
y
26
+ 9y
25
+ ··· − 6y + 1
c
4
, c
11
, c
12
y
26
+ 30y
25
+ ··· + 8y + 1
c
5
, c
8
y
26
+ 23y
25
+ ··· + 26y + 1
c
6
, c
10
y
26
+ 26y
25
+ ··· + 23y + 1
c
9
y
26
− 8y
25
+ ··· + 16y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994810 + 0.279825I
a = 1.20662 + 1.58702I
b = 0.227394 + 1.366040I
−3.35390 − 0.94845I −6.87984 + 3.64915I
u = 0.994810 − 0.279825I
a = 1.20662 − 1.58702I
b = 0.227394 − 1.366040I
−3.35390 + 0.94845I −6.87984 − 3.64915I
u = −0.896116 + 0.358125I
a = 1.82244 − 1.90249I
b = 0.10623 − 2.13069I
−11.06900 + 1.49966I −11.79695 + 3.82891I
u = −0.896116 − 0.358125I
a = 1.82244 + 1.90249I
b = 0.10623 + 2.13069I
−11.06900 − 1.49966I −11.79695 − 3.82891I
u = −0.182958 + 1.069700I
a = −0.165446 + 0.603831I
b = −0.326305 + 1.013770I
1.50865 − 1.30118I −4.13640 + 4.60269I
u = −0.182958 − 1.069700I
a = −0.165446 − 0.603831I
b = −0.326305 − 1.013770I
1.50865 + 1.30118I −4.13640 − 4.60269I
u = −0.539712 + 0.685386I
a = −0.568414 − 0.817881I
b = −0.385644 − 0.655112I
−3.16868 + 5.70923I 0.89618 − 5.43712I
u = −0.539712 − 0.685386I
a = −0.568414 + 0.817881I
b = −0.385644 + 0.655112I
−3.16868 − 5.70923I 0.89618 + 5.43712I
u = −0.873848 + 0.718674I
a = 0.595356 + 0.958868I
b = −0.046280 − 0.505395I
0.84766 + 2.74739I 6.98009 − 2.11826I
u = −0.873848 − 0.718674I
a = 0.595356 − 0.958868I
b = −0.046280 + 0.505395I
0.84766 − 2.74739I 6.98009 + 2.11826I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.041120 + 0.481650I
a = −1.27885 − 1.92900I
b = 0.732093 − 0.736920I
−5.41688 − 8.12687I −2.91620 + 10.98109I
u = 1.041120 − 0.481650I
a = −1.27885 + 1.92900I
b = 0.732093 + 0.736920I
−5.41688 + 8.12687I −2.91620 − 10.98109I
u = 0.873481 + 0.804316I
a = 0.336421 − 0.216727I
b = −0.064219 + 0.596287I
4.02040 − 3.00294I −13.3311 + 9.6327I
u = 0.873481 − 0.804316I
a = 0.336421 + 0.216727I
b = −0.064219 − 0.596287I
4.02040 + 3.00294I −13.3311 − 9.6327I
u = −1.095000 + 0.529832I
a = −0.88226 + 1.88566I
b = 0.625830 + 1.064040I
−1.34633 + 6.03466I 3.29288 − 4.61700I
u = −1.095000 − 0.529832I
a = −0.88226 − 1.88566I
b = 0.625830 − 1.064040I
−1.34633 − 6.03466I 3.29288 + 4.61700I
u = 0.645691 + 0.412052I
a = 1.59816 + 1.11692I
b = −0.636457 − 0.552346I
−3.99958 + 4.31687I 0.76169 − 4.27455I
u = 0.645691 − 0.412052I
a = 1.59816 − 1.11692I
b = −0.636457 + 0.552346I
−3.99958 − 4.31687I 0.76169 + 4.27455I
u = −1.154670 + 0.441862I
a = 0.85882 − 1.26098I
b = 0.385734 − 0.901560I
−5.49285 − 1.08973I −1.82174 + 3.24447I
u = −1.154670 − 0.441862I
a = 0.85882 + 1.26098I
b = 0.385734 + 0.901560I
−5.49285 + 1.08973I −1.82174 − 3.24447I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743428 + 0.117360I
a = 1.62838 − 1.59027I
b = −0.275262 − 0.830725I
−2.61520 − 0.29638I −3.41297 − 0.74904I
u = 0.743428 − 0.117360I
a = 1.62838 + 1.59027I
b = −0.275262 + 0.830725I
−2.61520 + 0.29638I −3.41297 + 0.74904I
u = 0.999411 + 0.755073I
a = −1.01604 − 1.23039I
b = 0.16796 − 1.63056I
−8.59776 − 3.03619I 7.54150 − 1.66230I
u = 0.999411 − 0.755073I
a = −1.01604 + 1.23039I
b = 0.16796 + 1.63056I
−8.59776 + 3.03619I 7.54150 + 1.66230I
u = −0.555636 + 0.302936I
a = 1.364820 + 0.228812I
b = −0.511074 + 0.745245I
0.84996 − 2.10170I 4.82287 + 3.44352I
u = −0.555636 − 0.302936I
a = 1.364820 − 0.228812I
b = −0.511074 − 0.745245I
0.84996 + 2.10170I 4.82287 − 3.44352I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 10u
25
+ ··· − 12u + 1)(u
120
+ 49u
119
+ ··· + 96657u + 5776)
c
2
(u
26
− 5u
24
+ ··· − 6u
2
+ 1)(u
120
+ u
119
+ ··· + 55u + 76)
c
3
(u
26
+ u
25
+ ··· − 6u + 1)(u
120
+ 15u
118
+ ··· + 8192u + 1024)
c
4
(u
26
− 2u
25
+ ··· − 2u + 1)(u
120
+ 3u
119
+ ··· + u + 2)
c
5
(u
26
− 3u
25
+ ··· + 13u
2
+ 1)(u
120
− 4u
119
+ ··· − 288u + 112)
c
6
(u
26
+ 13u
24
+ ··· + 3u + 1)(u
120
− u
119
+ ··· + 10311u + 1766)
c
7
(u
26
− 5u
24
+ ··· − 6u
2
+ 1)(u
120
+ u
119
+ ··· + 55u + 76)
c
8
(u
26
+ 3u
25
+ ··· + 13u
2
+ 1)(u
120
− 4u
119
+ ··· − 288u + 112)
c
9
(u
26
− 4u
24
+ ··· + 8u
2
+ 1)(u
120
− 7u
119
+ ··· + 3752u + 928)
c
10
(u
26
+ 13u
24
+ ··· − 3u + 1)(u
120
− u
119
+ ··· + 10311u + 1766)
c
11
, c
12
(u
26
+ 2u
25
+ ··· + 2u + 1)(u
120
+ 3u
119
+ ··· + u + 2)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 10y
25
+ ··· + 8y + 1)
· (y
120
+ 43y
119
+ ··· + 814266207y + 33362176)
c
2
, c
7
(y
26
− 10y
25
+ ··· − 12y + 1)(y
120
− 49y
119
+ ··· − 96657y + 5776)
c
3
(y
26
+ 9y
25
+ ··· − 6y + 1)
· (y
120
+ 30y
119
+ ··· + 22020096y + 1048576)
c
4
, c
11
, c
12
(y
26
+ 30y
25
+ ··· + 8y + 1)(y
120
+ 123y
119
+ ··· + 311y + 4)
c
5
, c
8
(y
26
+ 23y
25
+ ··· + 26y + 1)(y
120
+ 68y
119
+ ··· + 688512y + 12544)
c
6
, c
10
(y
26
+ 26y
25
+ ··· + 23y + 1)
· (y
120
+ 83y
119
+ ··· + 16685179y + 3118756)
c
9
(y
26
− 8y
25
+ ··· + 16y + 1)(y
120
+ y
119
+ ··· − 8464960y + 861184)
24
